Existing Works and Limitations. Hypothesis testing for MAB-collected data has been very recently considered in the ML literature [1]}, [2]}, with a strong focus on type-I error control. The predominant approach has been to establish theoretical conditions under which traditional Z-tests can lead to valid asymptotic inference (e.g., by restricting arms' allocation probabilities to lie within a range). Notably, while such constraints on the MAB algorithm may ensure CLT guarantees in adaptive settings, they may also considerably increase regret.
To illustrate this, Figure REF  displays the regret attainable by both standard TS (on which we build our AP-test),
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